If I remember correctly, the redesign of the mounting system for the Primo was made so that the router was pulled closer to the Z axis resulting in less of a cantilever. The Burly mounting plate will fit on the Primo. If you go this route, I suggest you print the Burly mounting plate with extra perimeters and then bore out the holes so you can use the Primo bolts and nut trips.
I too want to make my switching as easy as possible. My solution was to create a laser mount that fits down inside the Malita mount:
This mount is for the NEJE A40640 laser. I loosen the two screws on the Malita mount, slide the router out, and slide the laser in. I don’t know if the Ortur laser module is small enough to be mounted in a similar way. I provided the step files for this specific mount in this post.